Are you sure the exchange rate cancels itself out?
If I convert $100 into GBP, lets say I then have £200. If the % rate is 5%, then the first time, I get charged $5US, so I have $95 to convert and then I have £190. In the exchange back, the stem doesn't tell us the % is based upon one certain form of currency, so it seems that 5% would be levied upon the £190 as well, thus actually giving us £180.50 to exchange back into dollars. And if the exchange rate is 2:1 £:$, then £180.50 becomes $90.25. It doesn't cancel itself out. I'm not sure the wording of the question is exactly clear on how the commission % is calculated.
Either way you need to know the % commission otherwise in the exchange from £ back to $, you don't know how much is left after the first exchange, so you don't know how much is commission on the second exchange from £ to $.
We don't need exchange rate but we need commision %
convert $ to £
= 1000 *x*
= first converted amount received + first commision paid
= 1000*x (1-y/100)+ 1000*x*y/1000
reconvert amount 1000*x (1-y/100) £ to $ ( commision levied is y)
= second converted amount received+ second commision paid
= [1000*x (1-y/100) ] *1/x(exchange rate) * (1-y/100)
+ [1000*x (1-y/100) ] *1/x * y/100
second converted amount received\(= 1000 * (1-y/100) ^2\)
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